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If you experienced a significant personal injury (such as lung damage), I highly recommend you continue to look for legal counsel. While the first law firm you tried working with didn't work out, you can still consider working with other law firms licensed in Alaska (many WA state firms have attorneys licensed in AK as well).
Personal injury claims are based on expert testimony, this means you, or your attorney, will need to find a medical expert to testify as to the cause of your injury. The same (or a different) expert can then testify as to your projected future damages and cost of medical care.
Due to the complexity of these claims, I highly recommend that you retain a plaintiff's lawyer (also called trial attorneys). Fortunately the majority of these attorneys will provide you with a free consultation, and many will represent you on a contingency basis (they will advance the costs of litigation and legal services in exchange for a portion of your successful settlement or judgment).
You can find local attorneys using the State and Local Bar Association directories, or private directories such as www.AVVO.com; www.FindLaw.com; or www.Martindale.com (I personally find www.AVVO.com to be the most user friendly).
You will want to provide that to the next firm that takes your case.
(We cannot represent you here - our forum permits us to provide customers with general legal information, but not to provide legal representation or formal legal instruction. You really need a plaintiff's attorney to represent you in this matter, and while they will likely appreciate having a great deal of the data already put together, you need to contact them to allow them to do an evaluation of the case - and for you to decide whether or not you are comfortable with them handling your matter).